switching losses minimization and performance … · 2018-09-06 · dtc [4], dtc by using space...

© 2018 JETIR September 2018, Volume 5, Issue 9 www.jetir.org (ISSN-2349-5162)

JETIRA006260 Journal of Emerging Technologies and Innovative Research (JETIR) www.jetir.org 177

SWITCHING LOSSES MINIMIZATION AND

PERFORMANCE IMPROVEMENT OF PCC AND

PTC METHODS OF MODEL PREDICTIVE

DIRECT TORQUE CONTROL DRIVES WITH

VOLTAGE SOURCE INVERTER

Mr.Suraj r. Karpe1, Dr.S.A.Deokar2, Dr.A.M.Dixit3

Abstract- In Power Electronics, Predictive Current control (PCC) and Predictive Torque control (PTC) methods are advanced

control strategy. To control a Permanent Magnet Synchronous motor machine (PMSM), the predictive torque control (PTC)

method evaluates the stator flux and electromagnetic torque in the cost function and Predictive Current control (PCC) [1]

considers the errors between the current reference and the measured current in the cost function. The switching vector selected for

the use in IGBTs minimizes the error between the references and the predicted values. The system constraints can be easily

included [4, 5]. The weighting factor is not necessary. Both the PTC and PCC methods are most useful direct control methods

with PMSM method gives 10% to 30% more torque than an induction motor also not require modulator [3]. Induction motor work

on only lagging power factor means it can produce only 70-90% of torque produced by PMSM with same current. PCC and PTC

method with 2-level inverter using PMSM reduces 36% more THD in torque, speed and stator current compared to PCC and PTC

method with 2-level inverter using induction motor [21]. In this paper, switching loses minimization technique through THD

minimization. Switching losses are minimized because the transistors are only switched when it is needed to keep torque and flux

within their bounds. The switching pattern of semiconductor switches used to get better performance of multilevel inverter. This

scheme decreases the switching loss and also increases the efficiency & reduced losses. In this paper, the PTC and PCC methods

with voltage source inverter using PMSM are carried out and gives excellent torque and flux responses, robust, and stable

operation achieved compared to the PTC and PCC methods with 2-level voltage source inverter using IM. This novel method

attracted the researchers very quickly due to its straightforward algorithm and good performances both in steady and transient

states [8].

Index Terms—Electrical drives, predictive current control (PCC), predictive torque control (PTC).Permanent Magnet

Synchronous Motor (PMSM), Induction Motor (IM), Voltage Source Inverter (VSI).

INTRODUCTION:

DTC drive in last decade becomes one possible alternative to the well-known Vector Control of Induction Machines. Its main

characteristic is better performance with several advantages based on its simpler structure and control diagram. DTC (Direct

Torque Control) is described by the name, by directly controlled torque and flux and indirectly controlled stator current and

voltage [2]. The DTC has some advantages comparison with the conventional vector-controlled drives, like Approximately

sinusoidal stator currents and stator fluxes, High dynamic performance even at locked rotor and standstill, Absences of co-

ordinates transform, Absences of mechanical transducers, Current regulators, PWM pulse generation, PI control of flux and

torque and co-ordinate transformation are not required, Very simple control scheme and low computation time, Reduced

parameters sensitivity, superior dynamic properties. Conventional DTC has also some pitfall are possible problems during starting

and low speed operation, Variable switching frequency. To solve this demerit many research efforts have been made. Predictive

DTC [4], DTC by using space vector modulation, Band-constraining DTC [2] [11] are available methods for the torque ripple

reduction.

Predictive Current control (PCC) and Predictive Torque control (PTC) methods are promising methods [10]. Along reducing

torque ripples, the FCS-PTC method also illustrates a number of advantages, like the easy inclusion of constraints, easy

implementation, straightforward, algorithm and fast dynamic responses. The basic concept of model predictive direct torque

control (MPDTC) method is to calculate the required control signals in advance [6]. In the MPDTC method, pulse width

modulation is needless. The inverter model is required in the control method. During MPDTC, the PTC and PCC method

calculates all possible voltage vectors within one sampling interval and selects the best one by using an optimization cost function

[7]. To date, the PCC and PTC methods have been adapted in many operational situations and widely investigated, as given in the

articles [8], [9].

Model predictive control (MPC) in recent years has received convincingly contemplation and has gained demand in the power

electronics and industrial drives association. This MPC control strategy was first introduced in 1970, developed for process

control applications, is used commonly in the industry with numerous applications reported [4]. The basic perception of model

predictive control methods is that the decision of the controller is not centered on past state of the system, but with the predicted

behavior of the state variables and proper selection of the controlled variables either offline or online. MPC is also referred as

receding horizon control, as where its main perception is to reflect an infinite prediction horizon by constantly sliding the

prediction horizon. The current expansion and new orientation in the area of MPC mentioned in [5]. Due to simple in concept, the

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MPC also sometimes used to control the power converters because of its computational complexity is a burden to the processors.

Now a day due to the evolution of new high speed processor, the usage of MPC became an increase. In [6] the MPC is used to

control a VSI and multilevel inverter, where a discrete-time model of the VSI used to predict the forthcoming value of the load

current for all possible voltage vectors generated by the inverter. According to this, MPC has been widely used in many

applications in power electronics such as controlling various industrial drives like DC-DC converters [7], in matrix converters

[8]. MPDTC can be also used for speed control Permanent magnet synchronous motor and induction motor [9] [10] based on a

linearized state-space representation that describes the dynamic operation.

When MPC compared with the DTC method, the PTC method has two demerits: depend on speed and require higher

calculation time. Due to the implementation of the optimal cost function, the PTC method takes more time; this problem can be

solved easily, with better and faster microprocessing unit [10], [11]. The conventional PTC method for induction machine (IM)

and PMSM motor applications demands the rotor electrical speed in the prediction steps. The predicted stator current values are

dependent on the estimated speed and also on measured values of speed.

In this paper, the PTC and PCC methods with 2-level voltage source inverter using PMSM are carried out by simulation

method and compared with the PTC and PCC methods with 2-level voltage source inverter using induction motor. PCC and PTC

method with 2-level inverter using PMSM reduces 36% THD in torque, speed and stator current compared to PCC and PTC

method with 2-level inverter using an induction motor [10] [21]. In this paper, switching loses minimization technique through

THD minimization. Switching losses are minimized because the transistors are only switched when it is needed to keep torque

and flux within their bounds. This novel method attracted the researchers very quickly due to its straightforward algorithm and

good performances both in steady and transient states [8].

II. PMSM AND INVERTER MODEL

The mathematical model for the vector control of the PMSM can be derived from its dynamic d-q model which can be

obtained from model of the synchronous machine without damper winding and field current dynamics. The synchronously

rotating rotor reference frame is used so that stator winding quantities are transformed to the synchronously rotating reference

frame that is revolving at rotor speed. The model of PMSM without damper winding has been developed on rotor reference frame

using assumptions as Saturation is neglected, induced EMF is sinusoidal, core losses are negligible, there are no field current

dynamics. It is also be assumed that rotor flux is constant at a given operating point and concentrated along the d-axis while there

is zero flux along the q-axis, an assumption similarly made in the derivation of indirect vector controlled induction motor drives.

The rotor reference frame is chosen because the position of the rotor magnets determine independently of the stator voltages and

currents, the instantaneous induced emf and subsequently the stator currents and torque of the machine. When rotor references

frame are considered, it means the equivalent q- and d- axis stator windings are transformed to the reference frames that are

revolving at rotor speed. The consequences is that there is zero speed differential between the rotor and stator magnetic fields and

the stator q- and d- axis windings have a fixed phase relationship with the rotor magnet axis which is the d-axis in the

modelling[17,18].

The mathematical model of a PMSM given by complex equations in the rotor reference frame is as below:

Voltage equations are given by:

𝑉𝑑 = 𝑅𝑠𝑖𝑑 − 𝜔𝑟 𝜆𝑞 +𝑑𝜆𝑑

𝑑𝑡… .1, 𝑉𝑞 = 𝑅𝑠𝑖𝑞 − 𝜔𝑟 𝜆𝑑 +

𝑑𝜆𝑞

𝑑𝑡… . .2

Flux linkage are given by

𝜆𝑞 = 𝐿𝑞𝑖𝑞 … 3, 𝜆𝑑 = 𝐿𝑑𝑖𝑑 + 𝜆𝑓 … … 4

Substituting Equation 3 and 4 into 1 and 2, we get,

𝑉𝑞 = 𝑅𝑠𝑖𝑞 − 𝜔𝑟 (𝐿𝑑𝑖𝑑 + 𝜆𝑓) +𝑑(𝐿𝑞𝑖𝑞)

𝑑𝑡...5, 𝑉𝑑 = 𝑅𝑠𝑖𝑑 − 𝜔𝑟𝐿𝑞𝑖𝑞 . +

𝑑

𝑑𝑡(𝐿𝑑𝑖𝑑 + 𝜆𝑓).....6

Arranging equation 5 and 6 in matrix form,

(𝑉𝑞

𝑉𝑑) = (

𝑅𝑠 +𝑑𝐿𝑞

𝑑𝑡𝜔𝑟𝐿𝑑

−𝜔𝑟𝐿𝑞 𝑅𝑠 +𝑑𝐿𝑑

𝑑𝑡

) (𝑖𝑞

𝑖𝑑) + (

𝜔𝑟𝜆𝑓

𝑑𝜆𝑓

𝑑𝑡

)……7

The developed motor torque is being given by

𝑇𝑒 =3

2(

𝑃

2) (𝜆𝑑𝑖𝑞 − 𝜆𝑞𝑖𝑑)……8, 𝑇𝑒 =

3

4𝑃[𝜆𝑓𝑖𝑞 + (𝐿𝑑 − 𝐿𝑞)𝑖𝑞𝑖𝑑]……9,

𝑇𝑒 = 𝑇𝐿 + 𝐵𝜔𝑚 + 𝐽𝑑𝜔𝑚

𝑑𝑡…….10

Solving for rotor mechanical speed from equation 10, we get,

𝜔𝑚 = ∫ (𝑇𝑒−𝑇𝐿−𝐵𝜔𝑚

𝐽) 𝑑𝑡……11

And rotor electrical speed is

𝜔𝑟 = 𝜔𝑚 (𝑃

2)……12

Voltage Source Inverter:

In this work, a two-level voltage source inverter is applied to PTC and PCC methods. The topology of the inverter and its

feasible voltage vectors are presented in Fig. 1. The switching state S can be expressed by the following vector:




Fig. 1. Left: two-level voltage source inverter; right: voltage vectors

The stator voltage space vector representing the eight voltage vectors can be shown by using the switching states and the DC-

link voltage,𝑉𝑑𝑐, as:

𝑉𝑠(𝑆𝑎 , 𝑆𝑏 , 𝑆𝑐) = (2

3) 𝑉𝑑𝑐 (𝑉𝑎 + 𝑉𝑏𝑒𝑗(

2

3) + 𝑉𝑐𝑒𝑗(

4

3))...........13

Where 𝑉𝑑𝑐, is the DC-link voltage and the coefficient of 2/3 is the coefficient comes from the Park’s Transformation. Equation

(13) can be derived by using the line-to-line voltages of the AC motor which can be expressed as[10]:

𝑉𝑎𝑏 = 𝑉𝑑𝑐(𝑆𝑎 − 𝑆𝑏)…14 , 𝑉𝑏𝑐 = 𝑉𝑑𝑐(𝑆𝑏 − 𝑆𝑐)….15, 𝑉𝑐𝑎 = 𝑉𝑑𝑐(𝑆𝑐 − 𝑆𝑎)........16

The stator phase voltages (line-to-neutral voltages) are required & can be obtained from the line-to-line voltages as.

𝑉𝑎 = (𝑉𝑎𝑏 − 𝑉𝑐𝑎)/3….…17,𝑉𝑏 = (𝑉𝑏𝑐 − 𝑉𝑎𝑏)/3……18,𝑉𝑐 = (𝑉𝑐𝑎 − 𝑉𝑏𝑐)/3……..19

If the line-to-line voltages in terms of the DC-link voltage, Vdc, and switching states are Substituted into the stator phase

voltages it gives:

𝑉𝑎 = (1

3) 𝑉𝑑𝑐(2𝑆𝑎 − 𝑆𝑏 − 𝑆𝑐)…20, 𝑉𝑏 = (

1

3) 𝑉𝑑𝑐(−𝑆𝑎 + 2𝑆𝑏 − 𝑆𝑐)…21,

𝑉𝑎 = (1

3) 𝑉𝑑𝑐(−𝑆𝑎 − 𝑆𝑏 + 2𝑆𝑐)…22

Equation (3.14) can be summarized by combining with (3.12) as:

𝑉𝑎 = 𝑅𝑒(𝑉𝑠) = (1

3) 𝑉𝑑𝑐(2𝑆𝑎 − 𝑆𝑏 − 𝑆𝑐)…23, 𝑉𝑏 = 𝑅𝑒(𝑉𝑠) = (

1

3) 𝑉𝑑𝑐(−𝑆𝑎 + 2𝑆𝑏 − 𝑆𝑐)…24

𝑉𝑐 = 𝑅𝑒(𝑉𝑠) = (1

3) 𝑉𝑑𝑐(−𝑆𝑎 − 𝑆𝑏 + 2𝑆𝑐)…25, 𝑆 =

2

3(𝑆𝑎 + 𝑎𝑆𝑏 + 𝑎2𝑆𝑐).....26

where 𝑎 = 𝑒𝑗2𝜋

3 , Si = 1 means𝑆𝑖 ON, 𝑆�̅� means OFF, and i = a, b, c. The voltage vector V is related to the switching state S by

v = VdcS.....27

where Vdc is the dc-link voltage

V. SWITCHING LOSSES

The losses in the semiconductors can be divided into two parts, namely switching losses (arising when the devices are

switched on or off) and conduction losses (due to the ohmic resistance). These losses depend on the applied voltage, the

commutated current and the semiconductor characteristics. Observing that in a VSI inverter, the voltage seen by each

semiconductor is always half the total DC-link voltage leads to the Ideal switch turn-on (energy) loss

𝐸𝑜𝑛 = 𝑒𝑜𝑛1

2𝑉𝑑𝑐𝑖𝑝ℎ..........(10)

Where eon is a coefficient and iph is the phase current. For the Ideal switch, turn-off losses, a corresponding equation results

with the coefficient eoff. Typically, eoff is an order of magnitude larger than eon. For a diode, the switch-on losses are effectively

zero. The turn-off losses, however, which are reverse recovery losses, are linear in the voltage, but nonlinear in the commutated

phase current. Similar to the switching losses, the conduction losses also depend on the applied voltage and the phase current. The

DC link voltage is constant despite the neutral point fluctuations. The phase current is the sum of the current ripple and the

fundamental component, which in turn depends only on the operating point given by the torque and the speed, but not on the

switching pattern. Since the ripple is small compared to the fundamental current (typically in the range of 10% for a 3-level

inverter), the conduction losses can be considered to be independent of the switching pattern.

III. PREDICTIVE DIRECT CONTROL METHODS FOR PMSM

A. PCC: Predictive Current Control (PCC) uses only the predicted stator currents in the stationary reference frame in order to control

the multiphase drive. Current references are obtained in the rotating reference frame from an outer PI speed control loop and a

constant 𝑑-component current and then mapped in the stationary reference frame in order to be used in the cost function, as shown

in Fig. 2. This simple predictive controller scheme has been implemented in multiphase drives, with different number of

windings[10].




Fig.2 MPC based Predictive Current Control with an outer speed control loop

Aim is to generate a desired electric torque which implies sinusoidal stator current references in 𝑎-𝑏-𝑐 phase coordinates. In

the stationary --𝑥-𝑦 reference frame, the control aim is traduced into a reference stator current vector in the 𝛼-𝛽 plane, which is

constant in magnitude but changing its electrical angle following a circular trajectory, and depending on the implemented

multiphase machine, either null or non-null reference stator current vector in the 𝑥-𝑦 plane. For instance, if a three-phase machine

with distributed windings is implemented, the 𝛼-𝛽 stator current components contribute to torque production while 𝑥-𝑦 stator

current components do not, thus a zero reference is set for the 𝑥-𝑦 current components[20].

𝐽 = 𝐴|𝑖𝑠∝̿̿ ̿̿ | + 𝐵|𝑖𝑠𝛽̿̿ ̿̿ | + 𝐶|𝑖𝑠𝑥̿̿̿̿ | + 𝐷|𝑖𝑠𝑦̿̿̿̿ |…28

where each 𝛼-𝛽-𝑥-𝑦 current term is defined as:

|𝑖𝑠∝̿̿ ̿̿ | = 𝑖∗𝑠∝(𝑘 + 1) − 𝑖̂𝑠∝(𝑘 + 1) … . .29, |𝑖𝑠𝛽̿̿ ̿̿ | = 𝑖∗

𝑠𝛽(𝑘 + 1) − 𝑖�̂�𝛽(𝑘 + 1)…30

|𝑖𝑠𝑥̿̿̿̿ | = 𝑖∗𝑠𝑥(𝑘 + 1) − 𝑖̂𝑠𝑥(𝑘 + 1) … . .31, |𝑖𝑠𝑦̿̿̿̿ | = 𝑖∗

𝑠𝑦(𝑘 + 1) − 𝑖̂𝑠𝑦(𝑘 + 1)….32

The classical cost function is presented as follows:

𝑔𝑗 = ∑{|𝑖𝛼∗ − 𝑖𝛼(𝑘 + ℎ)𝑗| + |𝑖𝛽

∗ − 𝑖𝛽(𝑘 + ℎ)𝑗|}

𝑁

ℎ=1

… … . .33

Where j = 0 , . . 6 because a two-level voltage source inverter is applied in this system. All feasible voltage vectors are

presented in Fig. 1. It is easy to see that the inverter has eight different switching states but only seven different voltage vectors.

Thus, the cost function only needs to be calculated seven times. Therefore, gj has seven different values. In this values, the one

that minimizes the gj is selected as the output vector. h is the predictive horizon. In this work, only one step of PCC is considered,

thus h = 1. In the cost function, the state’s current values in αβ frame are required. The inverse Park transformation is presented

to satisfy this requirement as follows:

(𝛼𝛽) = (

𝑐𝑜𝑠(𝜃) −𝑠𝑖𝑛(𝜃)

𝑠𝑖𝑛(𝜃) 𝑐𝑜𝑠(𝜃)) (

𝑑𝑞

)……34

It was concluded that the PCC controller provided better transient state performance and low order harmonic minimization.

Where each 𝑑-𝑞-𝑥-𝑦 current term is defined as:

𝐽 = 𝑖�̿�𝑑 + 𝑖�̿�𝑞 + 𝑊𝑥𝑦[𝑖𝑠𝑥𝑦̿̿ ̿̿ ̿]….35

𝑖�̿�𝑑 = (𝑖∗𝑠𝑑

(𝑘 + 2) − 𝑖̂𝑠𝑑(𝑘 + 2))2, 𝑖�̿�𝑞 = (𝑖∗𝑠𝑞

(𝑘 + 2) − 𝑖̂𝑠𝑞(𝑘 + 2))2 ….36

𝑖�̿�𝑥𝑦 = (𝑖∗𝑠𝑥

(𝑘 + 2) − 𝑖̂𝑠𝑥(𝑘 + 2))2 + (𝑖∗𝑠𝑦

(𝑘 + 2) − 𝑖�̂�𝑦(𝑘 + 2))2 ….37

B.PREDICTIVE TORQUE CONTROL (PTC)

Fig.3 MPC based Predictive Torque Control with an outer speed control loop.




Predictive Torque Control (PTC) based on FCS-MPC for three phase two-level induction motor drives given in [20] is shown

in Fig. 3. It is done by an outer PI based speed control and an inner PTC and controlled variables are the stator flux and torque.

Torque reference is provided by an external PI, based on the speed error, while the stator flux reference has been set at its nominal

value for base speed operation. Then the cost function (10) is evaluated and the switching state with lower cost (𝐽) is applied to

the VSI. In order to improve PTC performance in [17] a modified cost function was presented, aimed to not only control stator

flux and produced torque but also limit the maximum achievable 𝛼-𝛽 stator currents to (𝑖𝛼𝛽−𝑀𝐴𝑋) and reducing harmonic

components in the 𝑥-𝑦 plane.

𝐽 =1

𝑇𝑛2 (𝑇𝑒

∗(𝑘) − 𝑇𝑒(𝑘 + 1))2

+1

ʎ𝑠𝑛2 (ʎ𝑠

∗(𝑘) − ʎ𝑠(𝑘 + 1))2….38

𝐽 =1

𝑇𝑛2 �̿�𝑒 +

1

ʎ𝑠𝑛2 ʎ̿𝑠 + 𝐾∝𝛽(|𝑖𝑠𝛼𝛽[𝑘 + 1]| > 𝑖𝛼𝛽−𝑀𝐴𝑋) +

1

𝑖𝑠𝑛2 |𝑖𝑠𝑥𝑦[𝑘 + 1]|

2…39

Where torque and flux terms are defined as:

�̿�𝑒 = (𝑇𝑒∗(𝑘) − 𝑇𝑒(𝑘 + 1))2, ʎ̿𝑠 = (ʎ𝑠

∗(𝑘) − ʎ𝑠(𝑘 + 1))2…40

In the predictive algorithm, the next-step stator flux �̂�𝑠(𝑘 + 1) and the electromagnetic torque �̂�(𝑘 + 1) must be

calculated. The stator flux prediction can be obtained [15,16]

.

�̂�𝑠(𝑘 + 1) = 𝜓𝑠(𝑘) + 𝑇𝑠. 𝑣𝑠(𝑘) − 𝑅𝑠. 𝑇𝑠. 𝑖𝑠(𝑘)……41

The electromagnetic torque can be predicted as

�̂�(𝑘 + 1) =3

2. 𝑝. 𝐼𝑚{�̂�𝑠(𝑘 + 1)∗. 𝑖̂𝑠(𝑘 + 1)}………42

The classical cost function for the PTC method is

𝑔𝑗 = ∑{|𝑇∗ − �̂�(𝑘 + ℎ)𝑗| + ʎ. |‖𝜓𝑠∗‖ − ‖�̂�𝑠(𝑘 + ℎ)𝑗‖|}

𝑁

ℎ=1

… . .43

IV. Implementation and Results

A. Simulation Results:

To verify the potential of the two schemes, a simulation comparison in MATLAB Simulink is performed. The

parameters of PMSM motor are given in Table 1. For all simulation, the motor characteristics will be utilized as below.

Stator phase resistance Rs (ohm) = 4.3

Armature Inductance (H) = 0.0001

Flux linkage established by magnets (V.s) = 0.05

Voltage Constant (V_peak L-L / krpm) = 18.138

Torque Constant (N.m / A_peak) =0.15

Inertia, friction factor, pole pairs [J (kg.m^2)] =0.000183

Friction factor F (N.m.s) = 0.001

Pole pairs p() =2

Initial conditions [ wm(rad/s) thetam(deg) ia,ib(A) ]= [0,0, 0,0]

Sampling Time (Sec) =1

Table. 1: PMSM parameters

The Matlab, Simulink model of PCC and PTC methods with PMSM using 2-level inverter shown in Fig.4(a) and Fig.4(b). and

the Simulink model of PCC and PTC methods with IM using 2-level inverter shown in Fig.5(a) and Fig.5(b). To achieve a

comparison between the two methods, the external PI speed controllers are configured with the same parameters. The simulation

results of the PCC method and the PTC method with PMSM and IM using 2-level inverter is shown in Fig.6, Fig.7 respectively.

From the pictures, we can see that both methods have good and similar behaviors at this point in the operation. The PCC method

has a slightly better current response; however, the torque ripples of the PTC method are lower than those of the PCC method.

The performances in the whole speed range are investigated in the simulations. The motor rotates from positive nominal speed to

negative nominal speed. During this dynamic process, the measured speed, the torque, and the stator current are observed. It is

clear that both methods have very similar waveforms [10]. They each have almost the same settling time to complete this reversal

process due to the same external speed PI parameters. The torque ripples of the PTC method are slightly lower than those of the

PCC method. From these simulations, we can conclude that two methods can work well in the whole speed range and have good

behaviors with full load at steady states. Induction motor work on only lagging power factor means it can produce only 70-90% of

torque produced by PMSM with same current.




Discrete,Ts = 1e-005 s.

powergui

v+-

v+-

v+-

v+-

VDC

Torque

Flux

Torque & Flux Estimator

Torque

(N.m)

0.85

157

GATE PULSE

Va

Vb

Vc

+Vin

-Vin

THREE PHASE

INVERTER

Switch

Step1

SPEED

&

TORQUE1

PULSE

mA

B

C

Tm

MOTOR

LINE VOLTAGES

INPUT DC

SUPPLY

-9

-K-

si-co

Q

D

alpha

Beeta

DQ to Alph-beta2

si-co

Q

D

alpha

Beeta

DQ to Alph-beta1

-pi/2

0

0.1

Constant

torque2

0.01

Constant

torque

T

T*

F

F*

w

Pulse

COST FUNCTION OPTIMIZATION

PI

<Rotor speed wm (rad/s)>

<Electromagnetic torque Te (N*m)><Electromagnetic torque Te (N*m)>

<Stator v oltage Vs_q (V)>

<Stator v oltage Vs_d (V)>

<Stator current is_q (A)>

<Stator current is_d (A)>

<Stator current is_a (A)>

Discrete,Ts = 1e-005 s.

powergui

f lux

w

ia

ib

current prediction

v+-

v+-

v+-

v+-

VDC

Flux

theta

Torque & Flux Estimator

Torque

(N.m)1

Torque

(N.m)

157

-157

TRIGGERING PULSE

Tiq*

id*

TORQUE & FLUX

GATE PULSE

Va

Vb

Vc

+Vin

-Vin

THREE PHASE

INVERTER

Switch

Step1

SPEED,

TORQUE & STATOR CURRENT

mA

B

C

Tm

MOTOR

LINE VOLTAGES

IPUT DC

SUPPLY

-9

-K-

si-co

Q

D

alpha

Beeta

DQ to Alph-beta3

si-co

Q

D

alpha

Beeta

DQ to Alph-beta2

si-co

Q

D

alpha

Beeta

DQ to Alph-beta1

-pi/2

0

-.1

Constant

torque2

0.01

Constant

torque

Ia*

Ia

Ib

Ib*

w

Pulse

COST FUNCTION OPTIMIZATION

PI

<Rotor speed wm (rad/s)>

<Electromagnetic torque Te (N*m)><Electromagnetic torque Te (N*m)>

<Stator v oltage Vs_q (V)>

<Stator v oltage Vs_d (V)>

<Stator current is_q (A)>

<Stator current is_d (A)>

<Stator current is_a (A)>

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

500

1000

1500

2000

2500

3000

3500

Time (seconds)

Roto

r_sp

eed_ptc

2

Fig.4(a) Fig.4(b)

Fig.4 Matlab Simulink model of PCC method with a)PMSM b) IM

Fig.5(a) Fig.5(b)

Fig.5 Matlab Simulink model of PTC method with a)PMSM b) IM

Fig.6 (a) Rotor speed in PCC

Fig.7 (a) Rotor speed in PTC

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-200

-150

-100

-50

0

50

100

150

200

250

Time (seconds)

Ro

tor_

sp

eed

_pcc2




0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-40

-30

-20

-10

0

10

20

30

40

Time (seconds)

sta

tor_

curr

ent_

ptc

2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-20

-10

0

10

20

30

40

50

60

70

Time (seconds)

ele

ctr

om

agnetic_to

rque_ptc

2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (seconds)

thd_ro

tor_

speed_ptc

2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

50

100

150

200

250

300

Time (seconds)

thd_ele

ctr

om

agnetic_to

rque_ptc

2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

10

20

30

40

50

60

70

Time (seconds)

thd_sta

tor_

curr

ent_

ptc

2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

1

2

3

4

5

6

7

8

9x 10

-5

Time (seconds)

roto

r_speed_ptc

_im

2

Fig.6 (b) Stator current in PCC

Fig.7 (b) Stator current in PTC

Fig.6 (c) Obtained torque in PCC

Fig.7 (c) Obtained torque in PTC

Fig.6(d) THD in rotor speed

Fig.7(d) THD in rotor speed

Fig.6(e) THD in electromagnetic torque

Fig.7(d) THD in electromagnetic torque

Fig.6 (f) THD in stator current

Fig.7 (f) THD in stator current

Fig.6 PCC using 2-level VSI with PMSM Fig.7 PTC using 2-level VSI with PMSM

Simulations results: speed, torque, and current Simulations results: speed, torque, and waveforms of PCC in steady state.

current waveforms of PCC in steady state.

Fig.8 (a) Rotor speed in PCC

Fig.9 (a) Rotor speed in PTC

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-20

-15

-10

-5

0

5

10

15

20

Time (seconds)

Sta

tor_

cu

rren

t_p

cc2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-50

-40

-30

-20

-10

0

10

20

30

40

50

Time (seconds)

Ele

ctr

om

ag

ne

tic_

torq

ue

_p

cc2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

1

2

3

4

5

6

7

8

9

Time (seconds)

thd

_ro

tor_

sp

eed

_pcc2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

5

10

15

Time (seconds)

thd_ele

ctr

om

agm

etic_to

rque_pcc2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

2

4

6

8

10

12

14

Time (seconds)

thd

_sta

tor_

cu

rren

t_p

cc2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

Time (seconds)

roto

r_sp

eed

_pcc_

im2




0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-200

0

200

400

600

800

1000Time Series Plot:<Stator current is_a (A)>

Time (seconds)

sta

tor_

cu

rren

t_p

cc_

im2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-1000

-900

-800

-700

-600

-500

-400

-300

-200

-100

0

Time (seconds)

sta

tor_

curr

ent_

ptc

_im

2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-30

-20

-10

0

10

20

30

40

50

60

Time (seconds)

ele

ctr

om

ag

ne

tic_

torq

ue

_p

cc_

im2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-0.18

-0.16

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

Time (seconds)

ele

ctr

om

ag

ne

tic_

torq

ue

_p

tc_

im2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8Time Series Plot:

Time (seconds)

thd

_ro

tor_

sp

eed

_pcc_

im2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Time (seconds)

thd

_ro

tor_

sp

eed

_ptc

_im

2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Time (seconds)thd_ele

ctr

magnetic_to

rque_pcc_im

2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Time (seconds)thd

_e

lectr

om

ag

ne

tic_

torq

ue

_p

tc_

im2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Time (seconds)

thd

_sta

tor_

cu

rren

t_p

cc_

im2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Time (seconds)

thd_sta

tor_

curr

ent_

ptc

_im

2

Fig.8 (b) Stator current in PCC Fig.9 (b) Stator current in PTC

Fig.8 (c) Obtained torque in PCC Fig.9 (c) Obtained torque in PTC

Fig.8 (d) THD in rotor speed Fig.9 (d) THD in rotor speed

Fig.8 (e) THD in electromagnetic torque Fig.9 (e) THD in electromagnetic torque

Fig.8 (f) THD in stator current Fig.9 (f) THD in stator current

Fig.8 PCC using 2-level VSI with IM Fig.9 PTC using 2-level VSI with IM

Simulations results: speed, torque, and current Simulations results: speed, torque, and waveforms of PCC in steady state.

current waveforms of PCC in steady state.

Both the PTC and PCC methods are most useful direct control methods with PMSM method gives 10% to 30% more torque

than an induction motor also not require modulator [3]. Induction motor work on only lagging power factor means it can produce

only 70-90% of torque produced by PMSM with same current. In this paper, switching loses minimization technique through

THD minimization. Total harmonic distortion (THD) has calculated successfully in this article by using MATLAB 2013 compare

to (10). The THD calculation of electromagnetic torque in the PCC and PTC Simulink model for PMSM with 2-level inverter is

shown in Fig.6 (d,e,f) and Fig.7 (d,e,f). The THD calculation of electromagnetic torque in the PCC and PTC Simulink model for

IM with 2-level inverter is shown in Fig.8 (d,e,f) and Fig.9 (d,e,f). The PCC and PTC method with 2-level inverter using PMSM

reduces 36% more THD in torque, speed and stator current compared to PCC and PTC method with 2-level inverter using an

induction motor shown detail in Table.3 [21].Graphical representation of % THD in rotor speed, electromagnetic torque and

stator current also shown in graph-1,2,3. The comparative issues between PCC and PTC also shown in Table.2. Switching losses

are minimized because the transistors are only switched when it is needed to keep torque and flux within their bounds. The

switching pattern of semiconductor switches used to get better performance of multilevel inverter. This scheme decreases the

switching loss and also increases the efficiency & reduced losses. In this paper, the PTC and PCC methods with 2-level inverter

using PMSM and IM are carried out and gives excellent torque and flux responses, robust, and stable operation achieved

compared to the PTC and PCC methods with 2-level voltage source inverter. This novel method attracted the researchers very

quickly due to its straightforward algorithm and good performances both in steady and transient states. The proposed scheme

shows better response as compared to the conventional one in terms of ripple in speed, torque and stator current during transient

conditions [10].




Sr. No

Different Methods

%THD in

Rotor Speed (wr) Torque (Te) Stator Current

1 PCC with PMSM using 2-level voltage

source inverter(VSI)

82.45% 68.60% 39.39%

2 PTC with PMSM using 2-level voltage


84.11% 41.40% 90.02%

3 PCC with IM using 2-level voltage


118.86% 104.14% 75.21%

4 PTC with IM using 2-level voltage


120.20% 77.38% 125.34%

Table.2: %THD Calculation comparison

V. CONCLUSION

In this paper, PCC and PTC methods of MPC family with 2-level inverter have been presented and discussed.The PCC and

PTC methods with 2-level inverter are direct control methods without an inner current PI controller or a modulator, the PCC

method with 2-level inverter has lower calculation time than the PTC method with 2-level inverter, fast dynamic response, and

Lower stator current harmonics than PTC. This advantage makes the PCC method more accurate for applications with longer

prediction horizons. From the test results, it is clear that the PCC method and the PTC method with 2-level inverter have very

good and similar performances in both steady and transient states. PTC method with 2-level inverter has lower torque ripples;

however, the PCC method with 2-level inverter is better when the currents are evaluated. This novel method attracted the

researchers very quickly due to its straightforward algorithm and good performances both in steady and transient states. Future

work is to test switched reluctance motor, and servo motor with 2-level VSI and multilevel inverter is applied to PCC and PTC

method, we can imagine that the PCC algorithm and PCC algorithm will greatly reduce the calculation time. The PCC method

shows strong robustness with respect to the stator resistance; however, the PTC method shows much better robustness with

respect to the magnetizing inductance.




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switching losses minimization and performance … · 2018-09-06 · dtc [4], dtc by using space...

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